Brazil coach Carlos Alberto Parreira did not feel the need to breathe a sigh of relief after watching his side book their place in the last 16.
The five-time winners needed second-half goals from Adriano and substitute Fred to overcome a battling Australia side.
But Parreira said: "We are happy to have qualified. It's a deserved win.
"We imposed both our style of playing, passing the ball around, and also imposed ourselves physically."
The coach added: "It is true that with three Australian forwards in our half it was more complicated, and we struggled at times but overall I think there are more positives than negatives."
Brazil, who turned in a lacklustre performance in their opening 1-0 win over Croatia, were far from their best again as they huffed and puffed against a gutsy Australian showing.
But Parreira warned: "It is normal that we are not in top form. We only played three friendlies before the finals and we are getting better and better little by little.
"We played better than we did against Croatia and we will play even better in the next one (against Japan)."
Goalscorer Fred also believes the holders will be able to express themselves now they have booked their place in the second round.
He said: "Thank God we were able to win. I'm really happy about scoring a goal so shortly (one minute) after I got on.
"We've qualified for the next round so now we'll be able to play more openly."